Why would the lookup table (of a table-driven artificial agent) need to store data at pixel precision?
A tabular system for agent decisions is a direct and simple map of percept to control choice. For each percept received, the agent looks up the percept and cross-references it to the action it should take. In order to construct this, you need to list all percepts in full detail, with the associated control choice.
Clearly that is not going to be feasible for the automated taxi example. No-one would think to build such a table to handle natural image inputs. That is the author's point.
However, a tabular structure is a reasonable theoretical construct for mapping an arbitrary discrete function, and also is practical for simple environments.
To answer your extended question:

Assuming $10^{600,000,000,000}$ is derived from $30 × 1080 × 720 × 24 × 8 × 3600$, what is the purpose of storing data in the look up table at pixel precision?

It is the only way to get a map from percept to control using a tabular system.
By proposing any kind of summarisation or approximation of the input-to-output function to solve this, you have gone beyond the capability of a tabular system. That again is the author's point.

Wouldn't storing higher level of details be enough to solve these kind of problems (ie, autonomous driving)?

If it is really obvious to you that this is the solution, then that's a good thing as you are thinking ahead. However, you should also consider what that means in terms of what you might be giving up, from a theoretical perspective. For instance, a tabular system can make radically different decisions based on very minor differences between percepts, whilst any form of processing of the inputs to make them easier to handle is necessarily going to remove information that might be important.